| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
02 Nov 2006 08:46:23 AM |
| Object: |
Pre-Geometry and Hawking's "Mind of God" |
IT FROM BIT
I went back to Penrose & Rindler's "Spinors and Space-Time".
1. A 2-component quantum BIT spinor |q> is a local object constructed at
a classical light cone at event P. Details are in Penrose's books.
2. An IT world tensor index u has two spinor indices A & A'.
3. For example, a spin 1 boson world vector field is an entangled pair
of spinor fermions.
4. The geometrodynamic tetrad field is an example of this! So is the
spin-connection field.
5. Ordinary local classical space-time uses localized spinors on the
same light cone. For example, the ordinary local coordinates are simply,
in Penrose's "spin network" substratum BIT pregeometry "Mind of God" the
diagonal of a set of matrices that do not commute - hence Connes'
"non-commutative geometry" that is still "local".
6. That is, let Su be the 2x2 Pauli spin matrix. Let q and q' be 2
independent qubits. We then have the matrices <q|Su|q'>. If the qubits q
and q' are LOCATED on the same light cone we get the ordinary
COMMUTATIVE LOCAL manifold of Einstein's classical theories of
relativity i.e.
dX^u(P,q) = <q(P)|Su|q(P)>
7. This is localized to a single light cone using the SAME spinor
flagged light ray on the light cone.
where ds^2 = (Minkowski)uvdX^udX^v is the local invariant - restrict to
special relativity for now.
8. The LOCAL non-commutative Connes space-time geometry uses 2
independent qubits q & q', i.e.
dX^u(P,q,q') = <q(P)|Su|q'(P)>
9. But we can go further and use NONLOCALLY ENTANGLED 2-qubit spinor
strings at separated events P and P' i.e.
dX^u(P,P',q,q') = <q(P)|Su|q'(P')>
10. We will need a spin-connection to parallel transport the spinors
from P to P' also there will be Young Tableau permutation symmetry
spanning P & P' - maybe even braid group beyond permutation group i.e.
KNOTs.
11. The 2-qubit Bell States of quantum teleportation play a special
role. The anti-symmetric spin singlet is like a nonlocal "time" T and
the three symmetric triplet states are like non-local space operators X,
Y, Z. T being antisymmetric may have something to do with the Arrow of Time?
.
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